单峰映射允许搓揉序列的Hausdorff维数和测度

Hausdorff Dimension and Measure of Admissible Kneading Sequences to Unimodal Mapping

利用Hausdorff维数和Hausdorff测度,对单峰映射的允许搓揉序列的集合给出定量刻画,证明了该集合在两个符号的单边符号空间中Hausdorff维数是1,1维Hausdorff测度是0.这与传统的定性分析相比,结果更有意义.

Using the tools of Hausdorff dimension and Hausdorff measure, we give quantitative version for the set of admissible kneading sequences to unimodal mappings. It is proved for the set that the Hausdorff dimension is 1 and the 1-dimension Hausdorff measure is zero in one-sided symbolic space with two symbols, which are more profound than those obtained by traditional qualitative analysis.